Question

Frederick needs to borrow $3000 for a down payment on a new car. His uncle decided to loan him the money as a 2.5% loan. Frederick doesn't want to pay more than $225 in interest. How many years does Frederick have to pay back the loan?

Answer 1

We are given that Frederick borrows $3000 at an interest rate of 2.5%. We will determine the time for this loan to gain $225. To do that we will use the following formula:

$I=\text{Prt}$

Where:

$\begin{gathered} I=interest \\ P=\text{ principal} \\ r=\text{ interest rate in decimal form} \\ t=\text{ time} \end{gathered}$

Now we solve for the time by dividing both sides by "Pr":

$\frac{I}{Pr}=t$

Now, the interest rate in decimal form is determined by dividing the percentage by 100:

$r=\frac{2.5}{100}=0.025$

Now we substitute the values:

$\frac{225}{3000\times0.025}=t$

Now we solve the operations:

$3=t$

Therefore, the time of the loan must be 3 years.